Quartiles are approximations. A more refined definition is the following For Low

ID: 3124468 • Letter: Q

Question

Quartiles are approximations. A more refined definition is the following

For Lower Quartile (25%):

Sort all observations in ascending order

Compute the position L1 = 0.25 * N, where N is the total number of observations.

If L1 is already a whole number (integer), the lower quartile is midway (average) between the L1-th value and the next one.

If L1 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the lower quartile.

For Upper Quartile(75%):

Sort all observations in ascending order

Compute the position L3 = 0.75 * N, where N is the total number of observations.

If L3 is a whole number, the upper quartile is midway (average) between the L3-th value and the next one.

If L3 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the upper quartile.

Please follow the above definitions in calculating the quartiles.

Note: each of the following problems is 15 points.

PROBLEM 2: average wait in minutes for a train:

45 4 5 5 6 12 17 10 10 11 8 15 16 9 0

PROBLEM 3: Quiz scores L

5 0 9 10 7 10 8 0 0 7 9 0 8

PROBLEM 4: Grades received in BUS310-01 course:

77 53 72 92 98 85 79 80

PROBLEM 5: Time to complete a specific job (in minutes)

10 14 12 11 12 8 8 7 6 5 9 4 5 13 14 10 9 10 12 10

For Lower Quartile (25%):

Sort all observations in ascending order

Compute the position L1 = 0.25 * N, where N is the total number of observations.

If L1 is already a whole number (integer), the lower quartile is midway (average) between the L1-th value and the next one.

If L1 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the lower quartile.

For Upper Quartile(75%):

Sort all observations in ascending order

Compute the position L3 = 0.75 * N, where N is the total number of observations.

If L3 is a whole number, the upper quartile is midway (average) between the L3-th value and the next one.

If L3 is not a whole number, change it by rounding up to the nearest integer. The value at that position is the upper quartile.

Sorting: 0,4,5,5,6,8,9,10,10,11,12,15,16,17,45

L1=0.25*15=3.75

L1 is not an integer, therefore, the changed value is 4.

L3=0.75*15=11.25

L3 is not an integer, therefore, change it to nearest whole number. L3=11